Index Card Notes

Post navigation

Nonobvious nonprimes

What’s the smallest nonprime that is not obviously nonprime? For Ramanujan the answer would have been in the thousands, but for the rest of us, I think it’s 91. The sequence of nonobvious nonprimes runs 91, 119, 133, 143, 161, 187,….

Here’s my reasoning. If a number is divisible by 2, 3, or 5, that’s obvious, and if it is 11 times a single digit, that’s obvious too. Also, perfect squares are pretty familiar. This leaves us with 7•13, 7•17, 7•19, 11•13, 7•23, 11•17,….